Testing critical phosphorus dilution curves for potato cropped in tropical Oxisols of southeastern Brazil

•The aim of this study was to validate a critical P dilution curve and P nutrition index (PNI).•Cultivars and P rates were assessed in nine field experiments in Oxisol soils.•A wide range in tuber yield and P concentration was observed across experiments.•Relative tuber yields were closely related to PNI.•The critical P dilution curve (Pc (%) = 0.391W−0.304) was validated. One of the challenges of potato (Solanum tuberosum L.) production is to minimize phosphorus (P) fertilization without negatively affecting the yield progress. Therefore, critical P dilution curves [Pc = acW−b; where Pc is the critical P concentration (%); ac is the critical plant P concentration (%) for a total dry matter (DM) biomass of 1 Mg ha-1; W is the total DM biomass expressed in Mg ha-1; and coefficient b is dimensionless and represents the ratio between the relative decline in plant P concentration and the relative crop growth rate] have been developed recently to improve P fertilization management in potatoes. The aim of this study was to test critical P dilution curves for potato cultivated in São Paulo State, southeastern Brazil. Nine field experiments were conducted in Oxisols with Presin values ranging from 8 to 70 mg dm-3 (very low to high). In each experiment, treatments were different P rates (ranging from 0 to 448 kg P ha-1) or the combination of different cultivars and P rates. Wide ranges in tuber DM yield (0.7-7.9 Mg ha-1) and plant P concentration (0.13-0.36 %) were observed before vine killing in response to P rates, cultivars, and site-years. Tuber DM yields were related to total DM biomass (R2 = 0.98), while P uptake was related to both total DM biomass and total plant P concentration (p < 0.01). Relative tuber DM yields at harvest were closely related to P nutrition index (PNI) (p < 0.01, R2 = 0.82) calculated with the critical P dilution curve previously reported for potato under higher yielding environments. These results validate the critical P dilution curve (Pc = 0.391W-0.304) as a useful diagnostic tool for improving the P fertilization of potato crops systems in the tropical region of Brazil.